LpL^p-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity

We study spectral properties of Schr\"odinger operators on \RR^d. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in \ZZ^d, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e.the normalised eigenvalue counting functions. The convergence holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq p< \infty$ is arbitrary.Comment: 15 pages; v2 has minor fixe

The Path Integral for 1+1-dimensional QCD

We derive a path integral expression for the transition amplitude in 1+1-dimensional QCD starting from canonically quantized QCD. Gauge fixing after quantization leads to a formulation in terms of gauge invariant but curvilinear variables. Remainders of the curved space are Jacobians, an effective potential, and sign factors just as for the problem of a particle in a box. Based on this result we derive a Faddeev-Popov like expression for the transition amplitude avoiding standard infinities that are caused by integrations over gauge equivalent configurations.Comment: 16 pages, LaTeX, 3 PostScript figures, uses epsf.st

QCD near the Light Cone

Starting from the QCD Lagrangian, we present the QCD Hamiltonian for near light cone coordinates. We study the dynamics of the gluonic zero modes of this Hamiltonian. The strong coupling solutions serve as a basis for the complete problem. We discuss the importance of zero modes for the confinement mechanism.Comment: 32 pages, ReVTeX, 2 Encapsulated PostScript figure

Transverse QCD Dynamics Near the Light Cone

Starting from the QCD Hamiltonian in near-light cone coordinates, we study the dynamics of the gluonic zero modes. Euclidean 2+1 dimensional lattice simulations show that the gap at strong coupling vanishes at intermediate coupling. This result opens the possibility to synchronize the continuum limit with the approach to the light cone.Comment: 15 pages, LaTeX, 3 figures (7 PS files

Static interactions and stability of matter in Rindler space

Dynamical issues associated with quantum fields in Rindler space are addressed in a study of the interaction between two sources at rest generated by the exchange of scalar particles, photons and gravitons. These static interaction energies in Rindler space are shown to be scale invariant, complex quantities. The imaginary part will be seen to have its quantum mechanical origin in the presence of an infinity of zero modes in uniformly accelerated frames which in turn are related to the radiation observed in inertial frames. The impact of a uniform acceleration on the stability of matter and the properties of particles is discussed and estimates are presented of the instability of hydrogen atoms when approaching the horizon.Comment: 28 pages, 4 figure

Temperature and Emission-Measure Profiles Along Long-Lived Solar Coronal Loops Observed with TRACE

We report an initial study of temperature and emission measure distributions along four steady loops observed with the Transition Region and Coronal Explorer (TRACE) at the limb of the Sun. The temperature diagnostic is the filter ratio of the extreme-ultraviolet 171-angstrom and 195-angstrom passbands. The emission measure diagnostic is the count rate in the 171-angstrom passband. We find essentially no temperature variation along the loops. We compare the observed loop structure with theoretical isothermal and nonisothermal static loop structure.Comment: 10 pages, 3 postscript figures (LaTeX, uses aaspp4.sty). Accepted by ApJ Letter

Quantum field theory of cooperative atom response: Low light intensity

We study the interactions of a possibly dense and/or quantum degenerate gas with driving light. Both the atoms and the electromagnetic fields are represented by quantum fields throughout the analysis. We introduce a field theory version of Markov and Born approximations for the interactions of light with matter, and devise a procedure whereby certain types of products of atom and light fields may be put to a desired, essentially normal, order. In the limit of low light intensity we find a hierarchy of equations of motion for correlation functions that contain one excited-atom field and one, two, three, etc., ground state atom fields. It is conjectured that the entire linear hierarchy may be solved by solving numerically the classical equations for the coupled system of electromagnetic fields and charged harmonic oscillators. We discuss the emergence of resonant dipole-dipole interactions and collective linewidths, and delineate the limits of validity of the column density approach in terms of non-cooperative atoms by presenting a mathematical example in which this approach is exact.Comment: 35 pages, RevTe

Aperiodic order and pure point diffraction

We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project schemes. We finish with a list of open problems.Comment: 14 page

MOST discovers a multimode delta Scuti star in a triple system: HD 61199

A field star, HD 61199 (V ~ 8), simultaneously observed with Procyon by the MOST (Microvariability & Oscillations of STars) satellite in continuous runs of 34, 17, and 34 days in 2004, 2005, and 2007, was found to pulsate in 11 frequencies in the delta Scuti range with amplitudes from 1.7 down to 0.09 mmag. The photometry also showed variations with a period of about four days. To investigate the nature of the longer period, 45 days of time-resolved spectroscopy was obtained at the Thueringer Landessternwarte Tautenburg in 2004. The radial velocity measurements indicate that HD 61199 is a triple system. A delta Scuti pulsator with a rich eigenspectrum in a multiple system is promising for asteroseismology. Our objectives were to identify which of the stars in the system is the delta Scuti variable and to obtain the orbital elements of the system and the fundamental parameters of the individual components, which are constrained by the pulsation frequencies of the delta Scuti star. Classical Fourier techniques and least-squares multi-sinusoidal fits were applied to the MOST photometry to identify the pulsation frequencies. The groundbased spectroscopy was analysed with least-squares-deconvolution (LSD) techniques, and the orbital elements derived with the KOREL and ORBITX routines. Asteroseismic models were also generated. The photometric and spectroscopic data are compatible with a triple system consisting of a close binary with an orbital period of 3.57 days and a delta Scuti companion (HD 61199,A) as the most luminous component. The delta Scuti star is a rapid rotator with about vsin i = 130 km/s and an upper mass limit of about 2.1 Msun. For the close binary components, we find they are of nearly equal mass, with lower mass limits of about 0.7 Msun.Comment: 11 pages, 14 figures, accepted by A&

Templeting of Thin Films Induced by Dewetting on Patterned Surfaces

The instability, dynamics and morphological transitions of patterns in thin liquid films on periodic striped surfaces (consisting of alternating less and more wettable stripes) are investigated based on 3-D nonlinear simulations that account for the inter-site hydrodynamic and surface-energetic interactions. The film breakup is suppressed on some potentially destabilizing nonwettable sites when their spacing is below a characteristic lengthscale of the instability, the upper bound for which is close to the spinodal lengthscale. The thin film pattern replicates the substrate surface energy pattern closely only when, (a) the periodicity of substrate pattern matches closely with the characteristic lengthscale, and (b) the stripe-width is within a range bounded by a lower critical length, below which no heterogeneous rupture occurs, and an upper transition length above which complex morphological features bearing little resemblance to the substrate pattern are formed.Comment: 5 pages TeX (REVTeX 4), other comments: submitted to Phys. Rev.Let